Tree-like process tensor contraction for automated compression of environments

TL;DR

This paper improves the efficiency of the ACE algorithm for simulating open quantum systems by introducing a tree-like contraction scheme for process tensor matrix product operators, significantly reducing computational cost.

Contribution

It presents a novel tree-like contraction method for PT-MPOs in ACE, enhancing speed while maintaining accuracy, and discusses strategies to mitigate associated errors.

Findings

Order-of-magnitude speedup over original ACE

Comparable compression efficiency and accuracy to original ACE

Effective for both bosonic and fermionic systems

Abstract

The algorithm "automated compression of environments" (ACE) [Nat. Phys. 18, 662 (2022)] provides a versatile way of simulating an extremely broad class of open quantum systems. This is achieved by encapsulating the influence of the environment, which is determined by the interaction Hamiltonian(s) and initial states, into compact process tensor matrix product operator (PT-MPO) representations. The generality of the ACE method comes at high numerical cost. Here, we demonstrate that orders-of-magnitude improvement of ACE is possible by changing the order of PT-MPO contraction from a sequential to a tree-like scheme. The problem of combining two partial PT-MPOs with large inner bonds is solved by a preselection approach. The drawbacks of the preselection approach are that the MPO compression is suboptimal and that it is more prone to error accumulation than sequential combination and compression. We therefore also identify strategies to mitigate these disadvantages by fine-tuning compression parameters. This results in a scheme that is similar in compression efficiency and accuracy to the original ACE algorithm, yet is significantly faster. Our numerical experiments reach similar conclusions for bosonic and fermionic test cases, suggesting that our findings are characteristic of the combination of PT-MPOs more generally.